The document is a comprehensive guide on coordinate geometry for Grade IX, covering concepts such as the Cartesian coordinate system, plotting points, and identifying quadrants. It explains the significance of coordinates in defining the position of points in a two-dimensional plane and includes various examples and exercises for better understanding. Additionally, it references NCERT textbooks and online sources for further learning.

1. For
Grade-IX
COORDINATE GEOMETRY
Chapter-3
By
Mr. Akash Yadav M.Sc, B.Ed
TGT(MATHS)
PM SHRI KV AFS BIDAR
Contact - 8829953881
Email – yadavakash0097@gmail.com

2. CONTENTS:
1. Introduction to Coordinate Geometry
2. Cartesian System
3. Plotting a Point in the Plane if its Coordinate are given
4.Summary

3. 1. Introduction to Coordinate Geometry:
What is a Geometry? The Branch of Mathematics Concerned with the properties
of and relationship between points, lines, planes, and figures
What is coordinate?
A pair of numbers that describe the position of a point
on a coordinate plane by using the horizontal and vertical
distances from the two reference axes.
Usually represented by (x,y) the x-value and y-value.
And O is the centre i.e (0,0) called origin.
What is Coordinate Geometry?
A coordinate geometry is a branch of geometry
where the position of the points on the plane is
defined with the help of an ordered pair of
numbers also known as coordinates.
The father of coordinate geometry was René Descartes

4. 2.Cartesian System/Cartesian Coordinate System :
What is Cartesian coordinate
system?
A Cartesian system is the
one which specifies a point
plotted uniquely on a plane
by a pair of numerical
coordinates, having a pre-
defined distance from the
two fixed perpendicular
coordinates, measured in the
same unit of length.

5. Cartesian Plane: What is a Plane?
Flat surface that extends infinitely along length and width.
WIDTH
Length
Cartesian is two dimensional grid formed
by drawing two number lines:
One is perpendicular to each other. i. e X-
By horizontal andY- ByVertical and two
point intersect at O (0,0)
ThenWhat is Cartesian Plane?

6. Abscissa and ordinate:
In the coordinate system, the term “Ordinate”
refers to the y -coordinate in (x, y). In short,
the distance along the y-axis is called the ordinate.
There is a difference in two terms
called coordinate and ordinate.The term “coordinate”
represents the position of the point along the line,
arc and so on, whereas the term “ordinate” represents
the value of a coordinate on the y-axis
The ordinate is the second component of an
ordered pair. For example, if (x, y) is an ordered pair,
then y is the ordinate here.An ordered pair is used to
denote a point in the Cartesian plane. It is the second
of the two terms (x, y) by which a point is defined, in
a system of fixed Cartesian Coordinate plane.
The first coordinate (x), in the plane, is called
the abscissa.The Cartesian system designates each
point in the XY plane, uniquely, by a pair of numerical
coordinates.These points are at the distances from the
two fixed axes, measured in the same unit of length.
A Is the Coordinate

7. What Is a Cartesian Coordinate Plane?
A Cartesian coordinate plane is a system of two perpendicular number lines on which we locate points.
The Cartesian coordinate plane consists of two perpendicular lines, x-axis and y-axis.
The horizontal line is called the x-axis.
The vertical line is called the y-axis.
The intersection point of these two axes is called origin and is represented by O.
The axes split through the origin, which is marked as 0 on the graph.
The side on the right of 0 is positive, while everything on the left is negative.
Similarly, as you go higher, the numbers are positive, while the negative numbers are written
below 0
The positive x-axis has positive numbers such as 1, 2, 3, 4,…..
The negative x-axis has negative numbers such as -1, -2, -3, -4,…..
The positive y-axis has positive numbers such as 1, 2, 3, 4,…..
The negative y-axis has positive numbers such as -1, -2, -3, -4,…..
A Cartesian coordinate plane can simply be called a coordinate plane or a plane.
It represents a 2-dimensional (2D) plane.
The Cartesian coordinate system is sometimes also referred as the Cartesian coordinate graph.

8. What is a Quadrants ?
Quadrant is the region enclosed by the
intersection of the X-axis and theY-axis.
On the cartesian plane when the two axes,
X-axis andY-axis, intersect with each other at
90º there are four regions formed around it,
and those regions are called quadrants. So,
every plane has four quadrants each bounded
by half of the axes. Each quadrant is
denoted by Roman numerals and named as
Quadrant I, Quadrant II, Quadrant III, and
Quadrant IV based on their position with
respect to the axes
Definition:A quadrant can be defined as a
region/part of a cartesian plane which is
obtained when the two axes intersect each
other. It is used to determine the position
of a point in a plane.

9. 3. Plotting a Point in the Plane if its Coordinate are Given
A point in a plane contains two components where order matters!
It comes in the form (x,y) where x comes first, and y comes second.
The x-value tells how the point moves either to
the right or left along the x-axis.
This axis is the main horizontal line of the
rectangular axis or Cartesian plane.
The y-value tells how the point moves either up
or down along the y-axis.
This axis is the main vertical line of the
rectangular axis or Cartesian plane.
The numbers on a coordinate grid are used to locate points.
Each point can be identified by an ordered pair of numbers; that is,
a number on the x-axis called an x-coordinate, and a number
on the y-axis called a y-coordinate. Ordered pairs are written in parentheses
(x-coordinate, y-coordinate)

10. How do you represent the points on the XY-Plane?
(x,y)
For Example -1
Write the coordinates of each of the points P,Q,R,S,T and O from the figure?
The coordinates of the points P,Q,R,S,T and O
P=(1,1) Q=(-3,0)
R=(-2,-3) S=(2,1) T=(4,-2)
O=(0,0)

11. 2. Points A(5,3) , B(-2,3) and D(5,-4) are the three vertices of a rectangle ABCD.
Plot these points on a graph paper and hence find the coordinates of the vertex C.

13. EXERCISE 3.1
1. How will you describe the position of a table lamp on your study table to another person?
Solution:
y
x
(25,30)
Lamp onTable
Fist Draw a x and y line and mark the points and measure the lamp distance
from x and y axis the distance of the lamp from y-axis is 30 cm and x-axis 25 cm

15. Solution:
W

16. Example1: William wants to throw a ball into a bucket which is placed on the coordinates (3, 10).
IfWilliam is standing on the coordinates (3, 5), how far will he have to throw the ball?
Solution
To calculate how farWilliam will have to throw the ball, we need to calculate the distance between
William and the bucket.The x-coordinate ofWilliam's location and the bucket is 3
Thus, they are on a line parallel to the y-axis.
Hence, the distance betweenWilliam and the bucket can be calculated as the difference of the y-
coordinates of both the points. 10−5=5units
Thus,Willam has to throw the Ball 5 unit way

17. ∴ a=3
Solution
We know that both the points P and Q lie on a line parallel to the x-axis, thus,
their y-coordinates are the same.
7−a=4
a=7 4
−
a=3
Example2: If point P (3,4) and point Q (5,7−a) lie on a line parallel to the x-axis, then what
is the value of a?
Example3: Jacob and Ethan want to make a frame using the coordinates (1,2),(3,2),(3,0),
(1,0).Based on the coordinates, Jacob says that the frame will be a square while Ethan says that the
frame will be a parallelogram. Can you identify who is right?
Solution
We need to draw the above coordinates on a Cartesian plane to check the shape they will form.
We can clearly see that the figure thus obtained is a
square as all the four sides are equal and all the
four interior angles are 90∘
There fore, Jocob is right.

18. EXAMPLE 1
Solution: Scale:
1 unit along X-axis=1CM
1 unit alongY-axis =1CM

19. EXAMPLE 2
Solution:

20. EXAMPLE 3
Solution:

21. 4 Summary:

22. References:
1. NCERT Text book.
2. Google sources.
THANK YOU